A wholesale electricity market design sans missing money and price manipulation

Energy Policy 134 (2019) 110988

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A wholesale electricity market design sans missing money and price manipulation

T

C.K. Wooa,∗, I. Milsteinb, A. Tishlerc, J. Zarnikaud a

Department of Asian and Policy Studies, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong Holon Institute of Technology, 52 Golomb Street, Holon, 58102, Israel c Coller School of Management, Tel Aviv University, Tel Aviv, 69978, Israel d Department of Economics, The University of Texas at Austin, 2225 Speedway, Austin, TX, 78712, USA b

ARTICLE INFO

ABSTRACT

Keywords: Electricity market design Wholesale competition Reliability differentiation Tolling agreements Missing money Price manipulation

Using reliability differentiation via tolling agreements with diverse heat rates and fuel types, we propose an efficient wholesale electricity market design under demand and supply uncertainty. Mainly based on North America's market experience, our proposed design adopts an independent system operator's (ISO's) existing practice of least-cost dispatch of heterogeneous generation units, real-time energy price determination and capacity rationing. It solves the missing money problem of inadequate incentive for thermal generation investment, without requiring the ISO to operate centralized capacity auctions, make capacity payments, set high energy price caps, or subsidize market entry. It preempts independent power producers' price manipulation in the ISO's real-time market for energy, thus easing the ISO's burden of market monitoring. It suggests two-part pricing of end-use consumption and power demand of a load serving entity's retail customers, thus meaningfully linking the wholesale and retail markets. It is applicable to countries that have implemented wholesale competition or are in the process of doing so. Hence, its policy implication is that it should be considered in the ongoing debate of electricity reliability and market competition.

JEL classification: D2 D43 L11 L94

1. Introduction Motivated by the global trend of electricity market reform and deregulation (Sioshansi, 2013), we propose an efficient wholesale market design under demand and supply uncertainty. Mainly based on North America's market experience,1 our proposed design's primary focus is electricity generation and wholesale market competition.2 It uses reliability differentiation via tolling agreements with diverse heat rates and fuel types to solve the thorny problems of missing money and price manipulation that can hamper an electricity grid's efficiency and re-

liability. As such, it is not a narrowly focused exercise of academic curiosity devoid of substantive policy relevance in a region's quest for a bright electricity future. The missing money problem occurs when a wholesale electricity market fails to provide adequate investment incentives for conventional generation units, including combined cycle gas turbines (CCGTs) and combustion turbines (CTs) (Joskow, 2013; Léautier, 2016).3 Exacerbating the missing money problem is the price reduction (aka merit order) effect of renewable generation like wind or solar that has zero fuel cost and displaces natural-gas-fired generation in an electric grid's

Corresponding author. E-mail addresses: [email protected] (C.K. Woo), [email protected] (I. Milstein), [email protected] (A. Tishler), [email protected] (J. Zarnikau). 1 Rich in details and pragmatic in nature, this paper draws heavily from the first author's publications based on research funded by several electric utilities and government agencies in North America, Israel and Hong Kong. As such, it has real-world applicability and relevance as detailed in Section 3 below. 2 For details on transmission topics like power flow, congestion, line loss and network security, see Stoft (2002), Kumar et al. (2005) and Wood and Wollenberg (2012). 3 Natural gas is the most popular fuel used by newly constructed generation units (Gal et al., 2017, 2019). Section 2 shows that our proposed market design can accommodate many heterogeneous generation technologies. We do not consider renewable generation's investment incentives which have been mainly driven by government intervention through generous tax credits, easy transmission access, above-market feed-in-tariffs, and legislated renewable portfolio standards (Alagappan et al., 2011; Zarnikau, 2011). ∗

https://doi.org/10.1016/j.enpol.2019.110988 Received 3 April 2019; Received in revised form 30 August 2019; Accepted 5 September 2019 0301-4215/ © 2019 Elsevier Ltd. All rights reserved.

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Abbreviations AS CAISO CEC CCGT CT DR DSS ERCOT FSL HR IPP ISO

kW kWh LLOE LLOP LSE MMBtu MW MWh NERC PJM RAR RTM VOLL

Ancillary services California Independent System Operator California Energy Commission Combined cycle gas turbine Combustion turbine Demand response Demand subscription service Electricity Reliability Council of Texas Firm service level Heat rate Independent power producer Independent system operator

least-cost dispatch (Woo et al., 2011a, 2013, 2014b, 2016a, 2017a, 2017b, 2018a; Zarnikau et al., 2014, 2019).4 The price manipulation problem occurs when independent power producers (IPPs) exercise their market power that can, even in the absence of a generation capacity shortage, cause abnormally high wholesale market prices (Wolfram, 1999; Borenstein et al., 2002; Woo et al., 2003a, 2006a). It likely worsens when an electric grid has transmission congestion that inhibits unrestricted power flows between low- and high-cost electrical zones (Joskow and Tirole, 2007; Woo et al., 2011b). To be fair, high market prices can occur sans market power abuse because of IPPs’ rational behavior (Milstein and Tishler, 2012). Contributing to market reform failures in the 1990s (Woo et al., 2003a, 2006a), the missing money and price manipulation problems persist today, as exemplified by Alberta's wholesale electricity market with an energy-only design (Brown and Olmstead, 2017). While a grid operator's diligent market monitoring has reduced generators' ability of price manipulation, the missing money problem continues to prevail in the huge electricity consuming states of California (Woo et al., 2016b) and Texas (Woo et al., 2012; Liu et al., 2016; Walker, 2019). Our proposed design is attractive because it does not require the various measures designed to enhance IPPs' investment incentives. Examples of such measures include centralized capacity auctions, capacity payments, high energy price caps, and subsidized market entry (Spees et al., 2013; Léautier, 2016; Cramton, 2017; Bublitz et al., 2019). It also preempts IPPs' market abuse in an independent system operator's (ISO's) real-time market (RTM) for energy, thus easing the ISO's burden of market monitoring.5 Our proposed design stems from reliability differentiation of wholesale transmission service (Woo et al., 1998) and retail end-use service (Chao and Wilson, 1987; Spulber, 1992; Wilson, 1993; Seeto et al., 1997; Woo et al., 2014a). In particular, it relies on the concept of demand subscription service (DSS) with fixed cost recovery (Woo, 1990, 1991). Under DSS, an end-use customer of an integrated utility must subscribe, before actual consumption, a firm service level (FSL in kW) that cannot be curtailed by the utility during a generation capacity shortage. The customer may, however, still see service interruptions due to local transmission and distribution failures. The utility's optimal generation capacity level is the total MW size of all FSL subscriptions plus a reserve margin to account for random plant outages, greatly

Kilowatt Kilowatt hour Loss of load expectation Loss of load probability Load serving entity Million British thermal units Megawatt Megawatt hour North American Electricity Reliability Council Pennsylvania-Jersey-Maryland Resource adequacy requirement Real-time market Value of lost load

simplifying the problem documented by Hobbs (1995) of utility resource planning under demand and supply uncertainty. A wholesale electricity market typically comprises an ISO, IPPs, load serving entities (LSEs), and a regulated transmission company (Woo et al., 2003a).6 Under open transmission access (Lusztig et al., 2006), wholesale electricity trading may occur bilaterally or through the ISO's centralized markets (Woo et al., 2013, 2017a, 2017b, 2018a; Zarnikau et al., 2014, 2019).7 We use the DSS concept to develop a new wholesale market design with the following key elements: (a) an ISO's RTM price determination and capacity rationing; (b) LSEs' two-part pricing of end-use consumption of their retail customers; (c) LSEs' optimal procurement plans for tolling agreements; and (d) LSEs' execution of the plans in (c) via decentralized procurement auctions. While these elements are not new, their meaningful integration via reliability differentiation under our proposed design is. Presently absent in North America's wholesale electricity markets is our proposed design's inducement of a LSE to self-reveal its reliability preference, enabled by the requirement that all LSEs under an ISO's jurisdiction must procure tolling agreements. This must-procure requirement is unrestrictive in practice because the total MW size of a LSE's procured agreements can range from zero MW to the peak MW unmet by the resources already in place (e.g., previously signed forward contracts and existing generation units). As a LSE preferring higher reliability tends to procure more MWs, the ISO can use the LSEs' procurement outcomes for efficient capacity rationing.8 Our proposed design is practical. Specifically, it uses an ISO's existing practice of (a) capacity rationing during a grid's critical hours9; and (b) RTM operation and price determination, like those described by

6 A LSE may be a local distribution company created by the divesture of a formerly integrated utility or a retail service provider emerged after the introduction of retail competition. For states (e.g., Oregon and Washington in the U.S.) and provinces (e.g., British Columbia and Quebec in Canada) that do not have an ISO, the regulated transmission company is the system operator. 7 A list of California's centralized markets and products is available at: http:// www.caiso.com/market/Pages/MarketProcesses.aspx A similar list for Texas is available at: http://www.ercot.com/mktinfo. 8 If a LSE's retail customers are mainly firms with onsite backup generation, the LSE likely prefers low reliability (Woo and Pupp, 1992). In contrast, if a LSE's retail customers are mostly high-income households with staying home members, the LSE likely prefers high reliability (Woo et al., 2014c and references thereof). As a result, a LSE's reliability preference may initially come from a general understanding of retail customers.Section 2.4.1 suggests a LSE's twopart retail pricing that has a demand charge ($/kW-month) for FSL subscription and a real-time energy charge ($/kWh) for energy consumption. Appendix 2 shows that the total MW of all FSL subscriptions helps set the total MW target of a LSE's procurement auction. 9 For a description of California's system alerts and emergency actions, see Woo et al. (2006c).

4 A dramatic case in point is an electric grid's occasional inability to fully absorb the non-dispatchable generation from solar and wind resources. Consequently, negative prices are used to induce dispatchable generation (e.g., CCGT) owners to curtail their output for maintaining the grid's real-time loadresource balance (Woo et al., 2016a). 5 A description of the California Independent System Operator's market monitoring is available at http://www.caiso.com/market/Pages/ MarketMonitoring/Overview.aspx.

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Woo et al. (2018a) for the California Independent System Operator (CAISO) and Zarnikau et al. (2014, 2019) for the Electric Reliability Council of Texas (ERCOT).10 It also uses a regulated LSE's Hopkinson tariff design for pricing retail consumption (Seeto et al., 1997) and auction process for procuring tolling agreements (Woo et al., 2004a, 2016b). Its practicality is further underscored by what the ISO does not use, including capacity payments and price caps (Léautier, 2016; Milstein and Tishler, 2019), subsidized market entry (Brown, 2018a), centralized capacity auctions (Brown, 2018b), and cost auditing of generation units (Munoz et al., 2018). As a result, it is applicable to countries that have implemented wholesale market competition (e.g., the U.S. and Canada in North America; Brazil and Chile in South America; Britain, Germany, Spain and Norway in Europe; Australia, New Zealand and Singapore in Asia Pacific) or are in the process of doing so (e.g., China, Israel, Japan and Korea in Asia). Our main contribution is our newly developed market design's reliability differentiation via tolling agreements based on many heterogeneous generation technologies with diverse heat rates and fuel types, unlike the single- and two-technology representations typically assumed in a Cournot market analysis (e.g., Milstein and Tishler, 2012, 2019; Gal et al., 2017, 2019). It underscores our methodological innovation of using tolling agreements to design an efficient wholesale electricity market under demand and supply uncertainty sans the twin problems of missing money and price manipulation. To place our contribution in the context of electricity reliability and market competition, our proposed design is an extension of mandatory reservation for firm transmission service under the pro forma tariff in Order 888 of the U.S. Federal Energy Regulatory Commission (Woo et al., 1998). It is a variation of the design proposal of Chao (2012) that uses demand-side forward contracts for priority service developed by Chao and Wilson (1987). Unlike the design proposal of Chao and Wilson (2004) that uses capacity call options with demand-based strike prices, it relies on heterogeneous tolling agreements with supply-based strike prices amenable to an ISO's least-cost dispatch, leading to a costbased RTM price determination that resembles those of South America's market designs analyzed by Munoz et al. (2018). Finally, it complements the analysis of Joskow and Tirole (2007), bridging the gap among various stakeholders, including: economists focused on competitive market mechanisms; engineers focused on an electric grid's physical attributes; industry practitioners focused on a market design's practicality; financial analysts focused on investment risks and return; LSEs focused on how to best serve their retail customers; retail customers focused on price stability, price reasonableness and service choice; IPPs focused on their financial performance; and regulators and policy makers focused on reliable electricity service at competitive prices, incentive compatibility and customer choice. The rest of the paper proceeds as follows. Section 2 formulates our proposed market design and presents our key findings, which are further discussed in Section 3. Section 4 concludes by recapping our proposed design's attractive properties, yielding the policy implication that the design should be considered in the ongoing debate of electricity reliability and market competition (Spees et al., 2013; Cramton, 2017; Coester et al., 2018; Conejo and Sioshansi, 2018; Newbery et al., 2018;

Bublitz et al., 2019). 2. Materials and methods 2.1. Overview Intended for a general audience, this section is an overview of our proposed design to introduce the key concepts used in the next three subsections. These concepts are tolling agreements, procurement auction, reliability differentiation, and an ISO's least-cost dispatch, RTM price determination, and capacity rationing. A tolling agreement is often based on a thermal generation unit (Eydeland and Wolyniec, 2003; Deng and Oren, 2006), a bilateral contract useful for managing a LSE's procurement cost and risk (Woo et al., 2006b).11 Its MW-size is limited by the underlying generation unit's installed capacity, consistent with the “no short sale” condition analyzed by Léautier (2016). It has terms and conditions that govern the underlying generation unit's forced outage rate and maintenance requirement.12 Under the assumption made in Section 2.2 that the ISO controls the unit's production, the unit's scheduled maintenance likely occurs in the mild-weather spring months of April and May when the grid has surplus capacity because of low hourly system demands.13 Hence, the LSE's optimal procurement plan described in Section 2.4.1 accounts for the supply uncertainty due to the unit's forced outage rate. After paying the agreement's upfront capacity price D ($/MW-year), a buying LSE has the right, but not the obligation, to obtain electricity from a selling IPP within the agreement's contract period at the strike price defined below14: $C/MWh = Heat rate HR (MMBtu/MWh) × Fuel price F ($/MMBtu). (1) The LSE exercises the right when the hourly spot market price P ($/MWh) exceeds C, earning an ex post per MWh variable profit of max (P – C, 0) that equals the per MWh cost saving from not buying electricity at high spot market prices (Woo et al., 2016b). We use C in equation (1) to characterize heterogeneous tolling agreements.15 For example, a CCGT-based agreement's C is lower than a CT-based agreement's because a CCGT's HR is lower than a CT's. This characterization is general, equally applicable to generation technologies with different heat rates and fuel types (e.g., natural-gas-fired vs. coal-fired generation). 11 The bilateral market for tolling agreements is not a centralized capacity market operated by an ISO like those in New York, New England and Pennsylvania-Jersey-Maryland (PJM). Hence, our paper is not about the merit of a centralized capacity market. 12 For the sake of clarity without any loss in generality, we assume that the unit's owner is responsible for maintenance, whose cost is included in the agreement's capacity price. 13 California's maintenance of thermal generation plants mainly occurs in these two months, an outcome reinforced by the state's inexpensive (< $20/ MWh) hydro power import during the Pacific Northwest's spring runoff (Woo et al., 2013, 2017b). 14 The variable HR measures a generation unit's efficiency in converting fuel (e.g., natural gas) to electricity. Both HR and F in equation (1) are stipulated in the bilateral agreement signed by the LSE and the IPP. While outside the purview of an ISO, they may be subject to prudence review of a local regulator (e.g., a state public utility commission) if the LSE is a regulated local distribution company (Woo et al., 2006c). For expositional simplicity, equation (1) intentionally ignores the per MWh costs for variable O&M, startup and ramping. Including these additional cost terms arithmetically complicates our market design analysis without the benefit of additional insights. 15 Equation (1) encompasses a demand response (DR) contract, which allows a LSE, after paying an upfront capacity price, to have the right but not the obligation, to obtain load reduction at $C/MWh from a DR supplier. Hence, our proposed design can incorporate DR contracts such as California's curtailable rate option (Moore et al., 2010) and hybrid capacity option (Woo et al., 2018b).

10 We focus on RTM prices even though CAISO and ERCOT have hourly dayahead market prices set on day d-1 for energy delivered on day d. As these dayahead prices are based on the day-ahead forecast of system conditions (Woo et al., 2017a; Zarnikau et al., 2019), they are not the market clearing prices for achieving an electric grid's real-time load-resource balances.Both CAISO and ERCOT use security-constrained economic dispatch algorithms to manage energy production, system power balance and network congestion, yielding 5-min nodal prices (Woo et al., 2018a; Zarnikau et al., 2014, 2019). Based on the theory of locational marginal pricing (Stoft, 2002), these nodal prices are the supply bid prices of the last dispatched units at the grid's numerous nodes. If these supply bid prices are excessively high due to IPPs' market abuse under lax market monitoring, they can cause inflated nodal prices.

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Fig. 1. The ISO's least-cost dispatch, RTM price determination and capacity rationing.

2018). Following the DSS's load curtailment strategy (Woo, 1990, p.71), the ISO's capacity rationing scheme under our proposed design is as follows. When the grid has a capacity surplus, all LSEs' demands are fully met. When the grid has a capacity shortage, each LSE receives its total procured capacity that is available during the shortage. Thus, the scheme precludes the inefficient outcome of load curtailment for some LSEs when the grid has a capacity surplus. It also implies that each LSE sees a load-resource balance constraint in a shortage hour. The ISO's capacity rationing is ex post efficient when it results in equal marginal benefits of electricity consumption for all LSEs (Woo et al., 2008). A sufficient condition for ex post efficiency is that LSEs' marginal benefits of electricity consumption exhibit similar time dependence and weather sensitivity (Woo, 1990; Spulber, 1992; Wilson, 1993). Satisfying this condition are the popular functional forms (e.g., double-log and linear) commonly used in electricity demand estimation (Woo, 1993; Woo et al., 2018c). Hence, the ISO's capacity rationing can empirically be as ex post efficient as real-time pricing proposed by Bohn et al. (1984). Matching the time sequence of the LSEs' resource procurement and the ISO's RTM operation,16 we use three steps to demonstrate our proposed market design's economic efficiency and adequate incentive for generation investment. In Step 1, the LSEs optimally procure tolling agreements before the realization of hourly RTM prices and weather conditions, while accounting for the agreements' underlying generation units' expected availability. In Step 2, the LSEs inform the ISO of their real-time electricity demands under the realized weather condition. In Step 3, the ISO uses the LSEs' procured agreements and real-time electricity demands for its least-cost dispatch, RTM price determination and capacity rationing. We analyze these steps recursively in Sections 2.2 to 2.4 below.

While C in equation (1) may fluctuate randomly (Gal et al., 2017, 2019), it is known with certainty on the day when the LSE decides whether to exercise the right to obtain electricity from the IPP. In short, a tolling agreement is an exotic option, comprising hourly capacity call options with daily varying strike prices (Deng et al., 2001). The missing money problem arises when a tolling agreement's expected variable profit cannot cover the underlying generation unit's returns on and of investment (Woo et al., 2016b). A tolling agreement's capacity price yields a stable revenue stream for an IPP, an important consideration in the IPP's ability to obtain project financing at reasonable terms (Stern, 1998). As shown in Section 2.4.2, its determination is based on a LSE's procurement auction that can provide adequate incentive for the winning IPP's long term investment. It decreases with C because the installation cost of a generation unit with a relatively low per MWh fuel cost (e.g., a CCGT) exceeds that of a generation unit with a relatively high per MWh fuel cost (e.g., a CT) (CEC, 2010). Our proposed design assumes competitively determined capacity prices for tolling agreements. Absent an active market for tolling agreements, such prices can come from a LSE's procurement auction (Laffont and Tirole, 1993), as currently done in California (Woo et al., 2016b). Based on a winning IPP's revealed preference, a signed agreement's capacity price presumably embodies adequate investment incentive that includes the returns on and of investment. Enabling our proposed design's reliability differentiation is the ISO's requirement that all LSEs under its jurisdiction must procure tolling agreements. This must-procure requirement is unrestrictive in practice because a LSE preferring higher reliability can procure more MWs. Further, a LSE that owns generation units or has previously signed power contracts can choose to procure between zero MW and the peak MW load unmet by the resources already in place. After confirming all LSEs' procured tolling agreements, the ISO uses a least-cost dispatch of the available generation units to serve each LSE's time-dependent demands (Chao, 1983; Stoft, 2002), yielding a RTM price solely based on the last dispatched unit's per MWh fuel cost. As shown by Fig. 1 below, the ISO's RTM price determination is not bidbased, thus preempting IPPs' RTM price manipulation (Munoz et al.,

2.2. Step 3: the ISO's least-cost dispatch, RTM price determination and capacity rationing We assume N LSEs that have agreed to delegate the right to the ISO for obtaining electricity at their procured tolling agreements' strike 16 This time sequence follows those of CAISO (Woo et al., 2018a) and ERCOT (Zarnikau et al., 2019).

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prices.17 The ISO performs a least-cost dispatch based on the LSEs' procured tolling agreements and real-time electricity demands. To do so, the ISO first confirms: (a) LSE n's procured MWs by tolling agreement type are {Kjn} for j = 1, …, J and n = 1, …, N; and (b) the hourly per MWh fuel cost of Kjn is Cjh in hour h = 1, …, H = 8,760 = number of hours in a calendar year.18 As there is no size limit for J, the procured agreements of all LSEs can encompass many heterogeneous generation technologies with diverse heat rates and fuel types. Moreover, the ISO's confirmation uses the signed tolling agreements submitted by the LSEs, not a cost audit of individual generation units. This makes sense because a tolling agreement is a commercial contract, with clearly stated terms and conditions that govern and enforce the buyer's and the seller's contractual obligations. The ISO cost ranks the agreements procured by all LSEs, resulting in a system hourly merit order that matches C1h < … < CJh.19 This

hourly merit order is time-invariant under two conditions. First, if all underlying generation units burn the same fuel (e.g., natural gas), it reflects these units' engineering-based heat rates of HR1 < … < HRJ. Second, nuclear and coal-fired units tend to have relatively low per MWh fuel costs and be dispatched before natural-gas-fired units (Woo et al., 2014b). To be fair, the hourly merit order can be time-dependent because of the low natural gas prices resulting from the “shale revolution”, occasionally causing natural-gas fired units to be dispatched before coal-fired units. As the ISO's RTM price determination given by equation (2) below is solely based on the hourly costs {Cjh}, the hourly merit order's time-dependence does not invalidate our subsequent analysis. Let Qh = Q (Ph, h, th) denote the grid's aggregate electricity demand of N LSEs at hourly price Ph and realized weather index th. An example of a weather index is the degree-hour commonly used in electricity demand studies, conveniently defined herein as th ≡ |hourly temperature – 65○F|.20 When the hourly temperature rises above or falls below 65○F, th increases, raising the grid's aggregate electricity demand through the LSEs' weather-sensitive loads.21 We define Qh = Σn q (Ph, h, th, n), where q (Ph, h, th, n) = LSE n's hourly electricity demand that does not a priori restrict th to be an additive or a multiplicative term. In contrast, a Cournot market analysis typically assumes that th is an additive term in the linear market demand function (e.g., Milstein and Tishler, 2012, 2019; Gal et al., 2017, 2019). The Step-2 analysis in the next section shows that q(•) is decreasing in Ph but increasing in th, in line with the empirics reported in the vast literature of electricity demand estimation.22 As a generation unit may become unavailable in hour h due to an unexpected equipment failure, we use Kh = Σn φ({Kjn},h) to denote the grid's total capacity made available in hour h by N LSEs' procurements of {Kjn}. Thus, φ(•) mimics a production function, transforming the procured MWs into available MWs. It is increasing in Kjn with ∂φ(•)/ ∂Kjn = βjh = 1 if Kjn is available in hour h; 0 otherwise. While βjh is known with certainty when the ISO makes its real-time dispatch decision, it is a random variable when the LSEs make their procurement decisions well ahead of the ISO's real-time dispatch. Section 2.4.1 shows how a generation unit's expected availability enters the LSEs' optimal procurement plans. Subject to the grid's capacity constraint of Qh ≤ Kh, the ISO's leastcost dispatch of generation units follows the hourly merit order so that the last dispatched unit j* obeys the condition of C1h < … < C(j*1)h < Cj*h < C(j*+1)h < … < CJh. Generation units with per MWh fuel costs above Cj*h are not dispatched in hour h and therefore have zero output. The ISO sets the RTM's market-clearing price ($/MWh) for hour h at the last dispatched unit's per MWh fuel cost:

17 The size of N is relatively small for California where retail competition is limited. In contrast, N is relatively large for Texas, a state with robust retail competition (Distributed Energy Financial Group, 2015; Woo and Zarnikau, 2019a). We assume that these LSEs aim to best serve their customers for the following reasons. First, if the retail market is highly competitive, unregulated LSEs compete rigorously to attract and retain customers. Second, if the retail market is dominated by a few unregulated LSEs, regulatory oversight and sanction restrain these LSEs' price gouging and other non-competitive practices. Finally, regulated LSEs are mandated to efficiently serve their customers at just and reasonable rates.To be sure, retail markets like those in the U.K. can be noncompetitive. While unregulated LSEs in these markets may like to price their services far above their marginal costs, their pricing behavior is constrained by the threat of regulatory sanction, the potential of retail market entrants, and the presence of regulated LSEs whom end-use customers can choose as their preferred suppliers. Hence, our wholesale market analysis remains valid, unless unregulated LSEs can freely exploit their customers with impunity. 18 Setting H at 8,760 reflects our focus of an annual analysis, which can be readily changed by modifying H's size. For example, a 10-year analysis would set H = 87,600 and entail discounted prices and costs to reflect the time value of money. We adopt the 60-min time scale mainly for notational simplicity. The analysis presented below is equally valid for the 5-min time-scale, involving arithmetic changes in the unit of measurement and time-interval definition. For example, the energy embodied in a 5-min demand of Z MW is (Z/12) MWh. Similarly, H becomes 12 × 8760 = 105,120 for the 5-min time scale. 19 Thanks to a very knowledgeable reviewer's remarkably detailed comment, we recognize that this hourly merit order is a simplification of an electric grid's real-time dispatch and operation for four reasons:(1) The merit order should account for LSE n's existing tolling agreements and dispatchable generation units.(2) The merit order should account for a tolling agreement's startup cost ($/MW per start), which is a fixed cost whenever the agreement's underlying unit starts up (Kumar et al., 2012). The startup cost's presence complicates an ISO's least-cost dispatch because if the unit has a large startup cost, the ISO may not dispatch the unit to meet its system load. Further, startup costs of the dispatched units require payments by LSEs to the ISO to ensure full cost recovery. As a result, the ISO may use an uplift charge in its transmission tariff to collect these payments (Lusztig et al., 2006). Each LSE then recovers its payment from its retail customers through a transmission service charge.(3) The merit order ignores other constraints such as those related to generator cycling. High spot market prices can occur under pure cost-based bidding if considerations of other generator parameters are included. For instance, grid conditions may require generators to come online for short periods of time, raising their per MWh costs to greatly exceed their simple fuel costs. In other cases, it may be economic for inflexible generators to remain online even if prices are lower than their costs, so that they are online in subsequent time periods with high spot prices.(4) The merit order ignores CO2 emissions, transmission congestion, and line loss and the ISO's need for operating reserves (i.e., ancillary services (AS)) for real-time grid operation. Including such details does not qualitatively alter our key findings. To wit, the merit order may be revised to reflect the per MWh costs that contain the cost effects of CO2 emissions (Woo et al., 2018a) and transmission congestion and line loss (Bohn et al., 1984). Similarly, the ISO's AS acquisition may come from the ISO's day-ahead assessment of system conditions, which is then used in the ISO's real-time security-constrained economic dispatch (Zarnikau et al., 2019).Notwithstanding the above reasons,

Ph = Cj*h.

(2)

The ISO's RTM price determination given by equation (2) replaces a Cournot electricity market's price outcome (Milstein and Tishler, 2012, (footnote continued) what matters here is that the resulting per MWh costs can still be used for the profit calculation based on equation (4) below. Consequently, the analysis in Sections 2.3 and 2.4 do not qualitatively depend on the computational nuances of the per MWh costs. 20 Changing our choice of 65○F does not alter our analysis in the rest of this paper. 21 For example, California is a summer peaking state whose high hourly demands occur on hot afternoons due to high air conditioning loads (Woo et al., 2016a). The same can be said for other summer peaking states like Arizona, Nevada, New Mexico and Texas. In contrast, winter-peaking states in the Pacific Northwest have high hourly demands that occur on cold winter evenings due to high space heating loads (Woo et al., 2013). 22 For literature reviews of electricity demand estimation, see Faruqui and Sergici (2010), Newsham and Bowker (2010) and Woo et al. (2018c). 5

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2019; Gal et al., 2017, 2019). IPPs cannot manipulate Ph in equation (2), chiefly because Ph is set sans IPPs' supply bidding (Munoz et al., 2018). Because Ph's volatility is the same as Cj*h's fuel-price-driven volatility (Gal et al., 2017), it is far less than the actual RTM price volatilities observed in states like California (Woo et al., 2018a) and Texas (Zarnikau et al., 2019).23 The ISO's capacity rationing scheme operates as follows. If Qh ≤ Kh, LSE n's ex post hourly consumption is the fully met q(•) for th < τh = weather index at which Qh = Kh24; otherwise, it is Knh = φ(•) = LSE n's ex post capacity available. As a result, the condition of Knh = φ(•) is LSE n's load-resource balance constraint in a shortage hour. The ISO's capacity rationing scheme implies that when the grid has an hourly capacity surplus, LSE n's ex post consumption may differ from ex post capacity available. Should the ISO use LSE n's excess capacity to meet other LSEs' demands, it would provide a profit refund to LSE n shown by equation (3) below. To aid our analysis of LSE n's optimal procurement plan in Section 2.4.1, we conveniently find here that the grid's loss-of-load probability in hour h is LOLPh = 1 – G(th = τh), where G(th) = cumulative distribution function of th ∈ (0, T = maximum degree hour). The grid's annual loss-of-load expectation is LOLE = 8,760 h × Σh LOLPh. As τh increases with Kh that depends on the LSEs' procurements, the grid's LOLE is endogenously determined under our proposed market design, unlike the administratively set LOLE criterion of 1-day-in-ten-years for North America's electricity industry (NERC, 2018). Fig. 1 illustrates the ISO's RTM price determination and capacity rationing. The solid green line portrays a hypothetical grid's generation stack of K1h MW of CCGTs and K2h MW of CTs available in hour h. The per MWh fuel costs for the CCGTs and CTs are C1h and C2h respectively. The red dashed lines are the grid's unconstrained demands in hour h by weather condition. The grid's RTM price is Ph = C1h under mild weather and Ph = C2h under extreme weather.25 Rather than allowing Ph to rise when the weather condition is extreme, the ISO uses capacity rationing in the shortage hour to resolve the difference between the grid's aggregate Qh at Ph = C2h and total available capacity at Kh = K1h + K2h. The ISO's capacity rationing portrayed by Fig. 1 can be ex post inefficient because unlike real-time pricing (Bohn et al., 1984; Woo et al., 2008), it does not guarantee equal marginal benefits of electricity consumption for all LSEs (Chao and Wilson, 1987; Woo, 1990; Spulber, 1992). This inefficiency, however, is likely small when the LSEs' marginal benefits of electricity consumption have similar time dependence and weather sensitivity (Woo, 1990; Spulber, 1992; Wilson, 1993), as implied by the popular functional forms (e.g., double-log and linear) used in electricity demand estimation (Woo, 1993; Woo et al., 2018c). Hence, the ISO's capacity rationing's ex post efficiency is expected to be numerically close to real-time pricing's. Our proposed design's financial settlement is as follows. LSE n pays Ph for each MWh bought from the ISO's RTM. The ISO's total RTM revenue is the sum of the energy payments made by all LSEs. The ISO uses the total RTM revenue to pay the fuel costs incurred by the dispatched generation units. Unless Ph = C1h = minimum RTM price for all hours, the ISO's total RTM revenue exceeds total fuel cost payment, resulting in a strictly positive operating surplus. The ISO refunds the surplus according to LSE n's ex post profit given below:

Vhn = (Ph – C1h) β1h K1n + … + (Ph – C(j*-1)h) β(j*-1)h K(j*-1)n.

(3)

Equation (3) reflects that at Ph = Cj*h, (K1n, …, K(j*-1)n) are profitable and Kj*n earns zero profit. Owing to the fuel cost payments and profit refunds, the ISO's RTM operation breaks even with certainty.26 A general representation of equation (3) is: Vhn = max(Ph – C1h, 0) β1h K1n + … + max(Ph – CJh, 0) βJh KJn,

(4)

implying that the real-time hourly marginal profit effect of Kjn is: ∂Vhn / ∂Kjn = max(Ph – Cjh, 0) βjh.

(5)

2.3. Step 2: a LSE's real-time energy demand assessment We assume LSE n passes αn% of Vhn to its retail customers. Hence, αnVhn may be seen as a “dividend payout” from LSE n to its retail customers in hour h. The following cases suggest αn is likely near 100%: (1) LSE n is a non-profit municipal utility; (2) LSE n is a local distribution company subject to the cost of service regulation; and (3) LSE n is an unregulated company operating in a highly competitive retail market. For the sake of generality, however, we allow αn to lie between 0% and 100%. The real-time energy demand curve q(Ph, h, th, n) comes from LSE n's benefit maximizing customers. Communicated to the ISO shortly (e.g., within 60 min) before the real-time dispatch, q(•) indicates the MWh amounts that LSE n is willing to buy at different RTM price levels in hour h when the already known weather index is th.27 To derive the unconstrained q(•) portrayed in Fig. 1 and used in the ISO's RTM price determination and capacity rationing, define the hourly maximum benefit from electricity consumption by LSE n's customers (Woo et al., 2008)28: Whn = [max ∫ p(q, h, th, n) dq – Ph qh] + αn Vhn,

(6.a)

= Uhn + αn Vhn,

(6.b)

where p(q, h, th, n) = marginal benefit of consuming q MWh of electricity for q ∈ (0, ∞) and Uhn = square-bracket term in equation (6.a). Equation (6.b) states that the maximum benefit Whn has two parts: (1) Uhn from consuming qh MWh of electricity; and (2) αn Vhn received from LSE n. Based on Woo (1990), we assume ∂p(•)/∂q < 0 and ∂p(•)/∂th > 0, reflecting that LSE n's marginal benefit decreases with electricity consumption but increases with the weather index. As LSE n's q(•) > 0, it satisfies Whn's first order condition of p(•) = Ph, lending support to the real-time marginal cost pricing rule (Chao, 1983; Bohn et al., 1984; Stoft, 2002; Woo et al., 2008). We use comparative statics to verify that q(•) is decreasing in Ph but increasing in th.

26 In the U.S., an ISO uses cost of service ratemaking (e.g., access and customer charges based on embedded costs) to recover its non-electricity costs for administration, management, market monitoring, billing, …, etc. (Lusztig et al., 2006). 27 An hourly electricity demand tends to be highly price inelastic because of its short run nature. The quantity demanded is mainly driven by its time dependence and weather sensitivity. LSE n's assessment of q(•) can be based on an estimation of electricity demand under time-of-use pricing, as exemplified by studies reviewed by Faruqui and Sergici (2010) and Newsham and Bowker (2010) for summer peaking LSEs and Woo et al. (2017c) for winter peaking LSEs. 28 As Fig. 1 shows that LSE n's unconstrained MWh demanded cannot be fully met at Ph = Cj*h in a shortage hour, the ISO's capacity rationing scheme enters LSE n's optimal procurement plan. Had we included LSE n's constrained MWh consumption in equation (6.a), we would have double-counted the effect of the expected hourly resource-balance constraint in Section 2.4.1 below.

23

Gal et al. (2017) document the fuel price volatilities of coal, oil and natural gas, which are much lower than the wholesale electricity price volatilities observed in North America. 24 The weather index threshold τh varies hourly because Qh is time-dependent. To wit, an electric grid's hourly demands during the 00:00 to 06:00 period are typically lower than those during the 06:00 to 24:00 period of a given day. 25 The market clearing price Ph in Fig. 1 is between C1h and C2h when the grid's hourly aggregate demand of Qh MW exactly equals the total CCGT capacity of K1 MW. This is an extremely rare technicality that we decide to ignore. 6

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2.4. Step 1: a LSE's optimal procurement of tolling agreements

($/MW-year) of an additional MW of capacity provided through tolling agreement type j. We next define Bjn = Σh∈S LOLPh λhn E[∂φ(•)/∂Kjn], which is LSE n's per MW-year expected marginal capacity value for tolling agreement type j. An estimate for Bjn is (Σh∈S LOLPh × VOLLhn × fj), where VOLLhn ≈ λhn is LSE n's value of lost load in shortage hour h; and fj ≈ E [∂φ(•)/∂Kjn] is the availability factor of agreement type j based on a generation technology's forced outage rate (Chao, 1983, p.184; Woo, 1990, p.75). This Bjn estimate makes sense because a 1-MW increase in firm capacity yields a reliability benefit of reducing LSE n's annual expected outage cost by an amount equal to (Σh∈S LOLPh × VOLLhn). Since the availability factor is fj < 1, the incremental MW's reliability benefit declines accordingly. Using the definitions of Aj and Bjn, we now state the key findings associated with LSE n's optimal procurement plan. First, if (Aj + Bjn) < Dj, Kjn = 0, reflecting that the per MW benefit (Aj + Bjn) is less than the per MW cost Dj (Chao, 1983, p.184). Second, suppose Kjn > 0 and (Aj + Bjn) = Dj. While the expected profit Aj is less than the capacity price Dj, LSE n is willing to pay a premium for the per MW reliability benefit of Bjn provided by Kjn. This finding justifies California's use of (Dj – Aj) > 0 to estimate the marginal capacity value of a new generation unit in a LSE's procurement plan (Sreedharan et al., 2012, p.117). It also implies that absent an additional revenue source, LSE n faces a per MW loss equal to (Dj – Aj), affirming the negative profit remark of Chao (1983, p.187). In an effort to break even, LSE n uses the procured agreements' capacity prices, as shown in Appendix 1, to calculate a monthly demand charge δn applicable to a retail customer's FSL subscription (Woo, 1990; Seeto et al., 1997).31 Hence, LSE n's two-part retail pricing has a Hopkinson tariff design, comprising a monthly demand charge ($/kWmonth) for FSL subscription and a real-time charge ($/kWh) for energy consumption. LSE n's recovery of the per MW loss of (Dj – Aj) through the retail demand charge δn does not alter LSE n's optimal capacity choice. This is because while δn affects LSE n's retail customers' FSL subscriptions made before actual consumption of electrical energy, it does not alter a tolling agreement's market-based profit Aj = Σh E[max(Ph - Cjh, 0) βjh]. Specifically, Aj is solely driven by the ISO's RTM price determination based on the least-cost dispatch in hour h of available generation units {Kjh} to serve the gird's aggregate demand Qh = Σn q(Ph, h, th, n), see Fig. 1 and discussion thereof. Clearly illustrating this point is KJn that has the highest per MWh cost CJh ≥ Ph for all h. Because max (Ph – CJh, 0) = 0, we find AJ = 0. Suppose the optimal KJn > 0. Absent a retail demand charge, LSE n suffers a per MW loss equal to DJ. As δn collects DJ on an annual basis, however, LSE n achieves full cost recovery. Using the same line of reasoning, we verify that δn helps LSE n to fully recover the per MW loss of (Dj – Aj) at Kjn > 0. We recognize that DSS may not have immediate acceptance by LSE n's retail customers. Hence, the two-part pricing's implementation uses an opt-in approach under which a retail customer's default monthly FSL subscriptions are the customer's monthly peak demands. If the customer desires curtailable service in exchange for a bill reduction, it can make monthly FSL subscriptions that are below its monthly peak demands (Moore et al., 2010; Woo et al., 2014a). Aided by advanced metering infrastructure (Woo et al., 2008), LSE n activates retail load curtailments through remote control in a smart grid environment (Woo et al., 2014a). Third, (Dj – Dj’) = (Aj – Aj’) + (Σh∈S LOLPh × VOLLhn) (fj – fj’) for Kjn > 0 and Kj'n > 0. When fj = fj’, (Dj – Dj’) = (Aj – Aj’). Hence, the capacity price difference between two chosen tolling agreements with identical availability should equal their market-based profit difference.

In Step 1, LSE n procures tolling agreements at competitively determined capacity prices. LSE n's procurement process answers the questions of “what to buy” and “how to buy”, a variation of theme of a LSE's management of procurement cost and risk (Woo et al., 2004a).29 We assume LSE n is risk-neutral. We later discuss the effect of risk aversion on LSE n's procurement plan in Section 4. 2.4.1. What to buy Answering the “what to buy” question requires LSE n to develop an optimal procurement plan. Suppose the capacity prices are {Dj}with D1 > … > DJ, reflecting that agreements with lower per MWh fuel cost forecasts have higher capacity prices than those with higher per MWh fuel costs forecasts.30 We assume that LSE n aims to best serve its customers, reflecting the policy mandate of a regulated LSE and the retail competition faced by an unregulated LSE. Hence, LSE n's objective function that includes the expectation of Whn and retained profit of (1 – αn) Vhn is: Ωn = Σh E[Whn + (1 – αn) Vhn] - Mn,

(7.a)

= Σh E(Uhn + Vhn) - Mn,

(7.b)

Where Mn = LSE n's total capacity payment = Σj Dj Kjn. Equation (7.b) is the result of recognizing equation (6.b) that states Whn = Uhn + αn Vhn. To find its optimal procurement plan, LSE n chooses {Kjn} to maximize Ωn, subject to the ISO's capacity rationing scheme. To solve LSE n's maximization problem, we recall Knh is LSE n's ex post consumption in a shortage hour. We also note that Knh does not vary with th ∈ (τh, T) because it is capped by the ISO's capacity rationing scheme. As a result, Knh's likelihood of occurrence is LOLPh. Further, E[φ(•) - Knh] = 0 is LSE n's constraint of expected load-resource balance in a shortage hour. Let S be the set of shortage hours. The Lagrangian with hourly multipliers {λhn} is: L = Ωn + Σh∈S LOLPh λhn E[φ(•) - Knh].

(8)

The Kuhn-Tucker conditions for LSE n's optimal procurement of Kjn ≥ 0 are: ∂L/∂Kjn = ∂Ωn /∂Kjn + Xn + Σh∈S LOLPh λhn E[∂φ(•)/∂Kjn] + Yn Dj ≤ 0; (9.a) Kjn ∂L/∂Kjn = 0;

(9.b)

∂L/∂λhn = LOLPh E[φ(•) - Knh] ≤ 0;

(9.c)

λhn ∂L/∂λhn = 0.

(9.d)

In equation (9.a), Xn and Yn are terms related to the marginal effect of Kjn on the endogenously determined τh because an increase in Kjn raises the capacity available at the system level. Specifically, Xn is the sum of: (a) Σh (Uhn + Vhn) g(τh) ∂τh/∂Kjn evaluated at q(•) and (b) Σh -(Uhn + Vhn) g(τh) ∂τh/∂Kjn evaluated at Knh, where g(th) = density function of th. As q(•) = Knh at th = τh, Xn = 0. Further, Yn = - Σh∈S λhn E [φ(•) - Knh] g (τh) ∂τh/∂Kjn = 0 because φ(•) = Knh in a shortage hour. Equation (9.a) to (9.d) yield market-based findings that match the efficient pricing and planning rules in Chao (1983) and Woo (1990) for social welfare maximization, affirming our proposed design's incentive compatibility (Laffont and Triole, 1993). To establish this claim, we first define Aj = ∂Ωn/∂Kjn = Σh ∂E (Vhn)/∂Kjn = Σh E[max(Ph - Cjh, 0) βjh] for all n ∈ (1, N), which is the market-based profit expectation 29

We do not consider the auction's timing and frequency. The “when to buy” and “how often” questions are implementation issues well beyond the intent and scope of our market design analysis. 30 These per MWh fuel cost forecasts can be based on the forward fuel prices in LSE n's planning period (Sreedharan et al., 2012).

31 There can be other demand charges for recovering LSE n's transmission and distribution costs. Examples of the retail tariffs of a regulated LSE are available at https://www.pge.com/tariffs/index.page.

7

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This profit-based finding mirrors the cost-based result of Chao (1983, p.183): the capacity cost difference should equal the expected fuel cost difference between two chosen generation technologies. Fourth, we verify that the optimal {Kjn} maximize social welfare Ω = Σn Ωn. Our verification entails (a) rewriting equation (8) as L = Σn Ωn + Σn Σh∈S LOLPh λhn E[φ(•) - Knh]; and (b) deriving the Kuhn-Tucker conditions for each LSE's optimal procurement of Kjn, which are the same as those given by equation (9.a) – (9.d). Finally, the LSEs' decentralized procurement decisions result in the socially optimal capacity level that does not require the ISO to know the LSEs' individual VOLL estimates (Woo, 1990, p.77). Appendix 2 shows that a LSE's total MW procurement target can readily be based generation units' forced outage rates and the LSE's retail customers' total FSL subscription at the demand charge derived in Appendix 1. This finding's practical importance is that while the VOLL estimates may come from customer outage cost estimation studies (e.g., Woo and Pupp, 1992; Woo et al., 2014c and references thereof), they are seldom available at the hourly level for all LSEs under the ISO's jurisdiction.

explains how our proposed design addresses the concerns of various stakeholders in a market design debate. From the perspective of energy economists, a wholesale electricity market can have the unintended consequences of market price manipulation and inadequate incentive for generation investment. Our proposed design mitigates these consequences through its fuel-cost-based RTM price determination by an ISO and procurement auctions by LSEs under the ISO's jurisdiction. From the perspective of electrical engineers, load-resource balance and resource adequacy are essential ingredients for reliable operation of an electric grid. Our proposed design provides such ingredients through its reliability differentiation enabled by an ISO's capacity rationing scheme and must-procure requirement for LSEs. From the perspective of industry practitioners, a market design proposal's conceptual merit must come with practical implementation. Our proposed design is practical, relying on an ISO's existing practice of least-cost dispatch, RTM price determination and capacity rationing. Further, its suggested two-part pricing of retail consumption follows the commonly used Hopkinson tariff design (Seeto et al., 1997). Finally, it shows how to value new capacity for determining the cost-effectiveness of a demand side management program (Sreedharan et al., 2012). From the perspective of IPPs, undesirable is a market environment that cannot provide adequate and stable revenue streams. As a result, an energy-only market's occasionally price spikes may be insufficient to induce generation investments. Our proposed design offers adequate and stable revenue streams via LSEs' procurement auctions. Further, unlike a forward contract's fuel cost risk that is borne by an IPP, a tolling agreement's fuel cost risk is borne by a LSE's retail end-users under our suggested two-part pricing of retail consumption. From the perspective of LSEs, the goal is to best serve their retail customers. Our proposed design assumes the same goal and is therefore consistent with these LSEs’ self-interests. From the perspective of retail end-users, price reasonableness, price stability and customer choice are preferable. Our proposed design's retail pricing is deemed reasonable based on a LSE's competitive procurement of tolling agreements and an ISO's fuel-cost-based RTM price determination. Further, the resulting RTM prices are expected to be far less volatile than those reported in California, Texas and other parts of North America (e.g., Alberta and Ontario in Canada; and New York, New England and PJM in the U.S.). Finally, our proposed design offers customer choice because a retail end-user can self-select its preferred reliability level through its FSL subscription and choose which LSE to be its preferred service provider. From the perspective of regulators and policy makers, reliable service at competitive prices, customer choice, incentive compatibility, and practicality are critical criteria for gauging a market design's merit. Our proposed design meets these criteria, as demonstrated by the analysis presented in Section 2.

2.4.2. How to buy Absent an active market for tolling agreements, LSE n uses a procurement auction. The auction process has three steps (Woo et al., 2004a, 2016b): (1) LSE n issues a request for proposal to announce its total MW target (e.g., 1,000 MW) and eligibility criteria for IPPs’ auction participation32; (2) interested IPPs then submit their tolling agreement offers; and (3) subject to cost benchmarking based on the long-run marginal cost of market entry (Orans et al., 2004; CEC, 2010), LSE n selects the winning offers to execute its optimal procurement plan found in Section 2.4.1. Aided by cost benchmarking, LSE n's procurement auction is expected to yield competitively determined capacity prices (Klemperer, 2004) that track the per MW-year capacity costs of new generation units (CEC, 2010). Successful Anglo-Dutch procurement auctions (Woo et al., 2003b, 2004b) further allay concerns of non-competitive capacity prices in a Cournot market setting (Munoz et al., 2018). Finally, the auction may include suppliers of demand response resources (Woo et al., 2014a) to counter the potentially non-competitive behavior of IPPs (Brown, 2018b). 3. Discussion Designing an efficient wholesale market is a well-documented challenge faced by energy economists, electrical engineers, industry practitioners, IPPs, LSEs, retail end-users, as well as regulators and policy makers. While its implementation uses the ISO's least-cost dispatch and capacity rationing and LSEs' procurement auctions and twopart pricing, our proposed design relies on market forces to induce socially optimal decisions made by IPPs, LSEs and retail customers. Specifically, IPPs decide what to bid when participating in LSEs' procurement auctions. LSEs decide what to buy in response to the ISO's real-time price determination and capacity rationing and their retail customers' FSL subscriptions and electricity consumption. Retail customers decide their FSL subscriptions and electricity consumption in response to the demand and energy charges that track wholesale prices for capacity and energy. Difficult to achieve under the extant market designs, these socially optimal decisions represent a major step forward in the ongoing market design debate. To be sure, regulators play an important role in shaping these decisions because they determine a grid's wholesale and retail market structures and rules. However, they do not centrally control the wholesale prices for capacity and energy. Nor do they dictate the MW amounts of tolling agreements differentiated by fuel type and heat rate that IPPs wish to sell and LSEs like to buy for kWh and kW resale to retail customers. The rest of this section 32

4. Conclusions and policy implications We conclude by recapping our findings reported in Section 2. First, our proposed design is a practical implementation of an ISO's least-cost dispatch, efficient RTM price determination and efficient capacity rationing. Second, it relies on market forces to achieve an electric grid's socially optimal capacity level with adequate investment incentives. Third, it does not require the ISO to operate centralized capacity auctions, use capacity payments, set high energy price caps, or subsidize market entry. Fourth, it eases the ISO's burden of market monitoring by preempting IPPs' RTM price manipulation. Finally, it suggests a LSE's two-part pricing that has a demand charge for retail FSL subscription and a real-time energy charge for retail energy consumption, thus meaningfully linking the wholesale and retail markets. When taken together, these properties yield the policy implication that our proposed market design should be considered in the ongoing debate of reliability and market competition.

Appendix 2 shows how LSE n can estimate its total MW target. 8

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We would be remiss had we failed to mention the following caveats of our proposed market design. These caveats do not invalidate our paper's key findings and policy recommendation; rather, they shape our future research agenda. The first caveat is that some retail customers of a LSE are prosumers with behind-the-meter generation resources (e.g., roof-top photovoltaic systems) (Parag and Sovacool, 2016). Hence, the LSE's retail demand needs to be modified to include the investment behavior of a prosumer (Woo and Zarnikau, 2017), yielding retail demands that are net of prosumers' behind-the-meter generation (Woo and Zarnikau, 2019b). The second caveat is that our paper does not consider the presence of a large scale development of intermittent renewable energy (e.g., solar and wind) (Coester et al., 2018; Newbery et al., 2018). Besides the approach used by Milstein and Tishler (2011), an alternative is to modify the capacity availability and LOLP formulae in Section 2.2. The third caveat is that we have not addressed the financial risk in an electricity grid dominated by renewable resources (Tietjen et al., 2016). A LSE's risk management, however, can be based on a profit analysis of tolling agreements (Woo et al., 2016b) and a calculation of efficient frontiers (Woo et al., 2006b). Relative to a risk-neutral LSE, a risk-averse LSE likely procures more agreements with higher capacity prices, leading to the LSE's higher expected cost but lower cost risk (Woo et al., 2004a). The fourth caveat is that LSEs' pass-through of the procured tolling agreements' capacity costs shifts IPPs' investment risks to retail customers. Specifically, declining retail demands can cause the procured agreements to become stranded assets, burdening retail customers with large capacity cost commitments (Woo et al., 2003c). The problem of stranded assets, however, may be mitigated by LSEs' procurement of tolling agreements with relatively short contract lengths (e.g., not more than three years), similar to the contract lengths commonly used by centralized capacity auctions in the U.S. Unfortunately, this mitigation strategy may also discourage IPPs from making long-term investments in new power plant construction. As a result, the relationship between thermal generation's investment incentive and tolling agreements' contract lengths is an important topic for future research in wholesale market design. The fifth and final caveat is that given the diverse perspectives of the various stakeholders, our proposed design may not be widely acceptable because it limits market participants to certain types of contracts, prevents wholesale market participants from RTM bidding, recommends retail two-part pricing, possibly causes stranded assets, and requires advanced metering infrastructure to support a smart grid's operation efficiency and reliability management. This caveat is nontrivial, thus rationalizing our recommendation that our proposed design should be considered, rather than adopted, in the ongoing debate of reliability and market competition.

(1) Suppose LSE n's optimal procurement plan includes KJn > 0. Under the ISO's RTM price determination, the maximum Ph is C1h. As a result, AJ = 0 because max(Ph – CJh, 0) = 0 for all hours. LSE n's marginal capacity value is μn = (Σh∈S LOLPh × VOLLhn) fJ = DJ. Hence, LSE n sets its monthly demand charge at δn = DJ ÷ (12 months × 1000 kW per MW). (2) Suppose KJn = 0 and all chosen agreements' underlying technologies have the same availability factor f. As μn = (Σh∈S LOLPh × VOLLhn) f = Dj – Aj = D - A for all chosen agreements, δn = (D – A) ÷ (12 months × 1000 kW per MW). (3) Suppose KJn = 0 and all chosen agreements' underlying technologies have different availability factors. An estimate for μn is the arithmetic average of (Σh∈S LOLPh × VOLLhn) fj, the same as the arithmetic average of (Dj – Aj). Hence, δn = arithmetic average of (Dj – Aj) ÷ (12 months × 1000 kW per MW). As tolling agreements' underlying generation units have forced outages, these charges need to be adjusted upward using the multiplicative scalar (1/f) > 1, where f = average availability factor of the generation technologies likely used by the interested IPPs in Step 2. The resulting adjusted demand charges help pay for the cost of a grid's reserve margin derived in Appendix 2 below. Appendix 2. LSE n's procurement target LSE n's total MW target is an estimate based on the retail customers' FSL subscriptions under the DSS's opt-in approach noted in Section 2.4.1. The estimate is (MWFSL/f), where MWFSL = total MW size of all FSL subscriptions unmet by LSE n's resources already in place; and f = average availability factor of the generation technologies likely used by the interested IPPs in Step 2. Since CTs and CCGTs dominate new plant construction in North America, an estimate for f is 0.95 based on these generation units' forced outage rates reported in CEC (2010, p.C-10). This high f estimate implies that a region's resource adequacy requirement (RAR) can be as low as (1/f) = (1/0.95) ≈ 106%, well below California's current RAR of 115% (Woo et al., 2016b, p.52). Corresponding to the 106% RAR is a reserve margin of ~6%. A large decrease in a region's RAR, however, is likely imprudent because the target estimation portrayed here has not considered transmission-related issues such as line failures, congestion and network security. Nevertheless, a potentially large RAR reduction highlights the resource benefit of knowing, in advance and with certainty, a retail customer's demand for firm power (= FSL subscription) in a shortage hour. References Alagappan, L., Orans, R., Woo, C.K., 2011. What drives renewable energy development? Energy Policy 39, 5099–5104. Bohn, R.E., Caramanis, M.C., Schweppe, F.C., 1984. Optimal pricing in electrical networks over space and time. RAND J. Econ. 15, 360–376. Borenstein, S., Bushnell, J.B., Wolak, F.A., 2002. Measuring market inefficiencies in California's restructured wholesale electricity market. Am. Econ. Rev. 92 (5), 1376–1405. Brown, D.P., 2018a. The effect of subsidized entry on capacity auctions and the long-run resource adequacy of electricity markets. Energy Econ. 70, 205–232. Brown, D.P., 2018b. Capacity payment mechanisms and investment incentives in restructured electricity markets. Energy Econ. 74, 131–142. Brown, D.P., Olmstead, D.E.H., 2017. Measuring market power and the efficiency of Alberta's restructured electricity market: an energy-only market design. Can. J. Econ. 50 (3), 838–870. Bublitz, A., Keles, D., Zimmermann, F., Fraunholz, C., Fichtner, W., 2019. A survey on electricity market design: insights from theory and real-world implementation of capacity remuneration mechanisms. Energy Econ (in press). CEC, 2010. Comparative Costs of California Central Station Electricity Generation. Report CEC- 200-2009-07SF. California Energy Commission, Sacramento, California Available at: http://www.energy.ca.gov/2009publications/CEC-200-2009-017/ CEC-200-2009-017-SF.PDF, Accessed date: 6 March 2019. Chao, H.P., 1983. Peak load pricing and capacity planning with demand and supply uncertainty. Bell J. Econ. 14 (1), 179–190.

Acknowledgements This paper benefits from the helpful comments of D. Brown, H.P. Chao, Y. Chen, F. Kahrl, R. Orans, A. Yatchew, and two very diligent and knowledgeable reviewers. We thank M. Marchant for her copyediting and proofreading. C.K. Woo's research is funded by the Faculty of Liberal Arts and Social Sciences of the Education University of Hong Kong. The paper is part of J. Zarnikau's ongoing research on electricity markets at The University of Texas at Austin. Without implications, all errors are ours. Appendix 1. LSE n's retail demand charge Assuming no generation forced outages for the time being, the calculation of LSE n's retail demand charge ($/kW-month) applicable to a LSE's retail customers' FSL subscriptions may use one of the following three approaches: 9

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